One-dimensional quantum walks with one defect

Abstract

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the non negative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities at the origin.

References in corpus (7)

• One-Dimensional Three-State Quantum Walk
• The Analytic Theory of Matrix Orthogonal Polynomials
• Localization of Two-Dimensional Quantum Walks
• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• Dynamical Localization for Unitary Anderson Models
• Recurrence of biased quantum walks on a line
• Localization of an inhomogeneous discrete-time quantum walk on the line

Cited by in corpus (3)

• Limit measures of inhomogeneous discrete-time quantum walks in one dimension
• Return probability of one-dimensional discrete-time quantum walks with final-time dependence
• Limit Theorems for the Discrete-Time Quantum Walk on a Graph with Joined Half Lines